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A farmer is considering to buy a wind turbine to generate his own electricity.
A farmer is considering to buy a wind turbine to generate his own electricity. The power generated by a turbine receiving wind at the speed of v is given by P(v) = (min{max{v − 2, 0}, 10}) ^3 / 10 when the wind speed is less than 20 meters per second. If the wind blows faster than 20 m/s, the turbine shuts down and no energy is produced. Unfortunately, the turbine manufacturer forgot the specify the units of power but the farmer suspects the units to be either in Watts or kilo Watts. a) What are cut-in speed and cut-out speed according to this particular P(v) expression? b) Let vci and vco be the cut-in and cut-out speeds, and specialize the power expression only for speeds between vci and vco. Consider only the portion of power that increases in the wind speed and note the multiplier of v 3 down. c) Using the multiplier in b) and assuming an air density of 1.2 kg/m3 and that P(v) is in Watts, find the radius of blades. What would the radius of blades be if the power is in kilo Watts? Based on the radii computed, comment if P(v) should be in Watts or kilo Watts
